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The canonical equation of adaptive dynamics for life histories: from fitness-returns to selection gradients and Pontryagin's maximum principle.

Metz, Johan A Jacob; Staňková, Kateřina and Johansson, Jacob LU (2015) In Journal of Mathematical Biology 74(4). p.1125-1152
Abstract
This paper should be read as addendum to Dieckmann et al. (J Theor Biol 241:370-389, 2006) and Parvinen et al. (J Math Biol 67: 509-533, 2013). Our goal is, using little more than high-school calculus, to (1) exhibit the form of the canonical equation of adaptive dynamics for classical life history problems, where the examples in Dieckmann et al. (J Theor Biol 241:370-389, 2006) and Parvinen et al. (J Math Biol 67: 509-533, 2013) are chosen such that they avoid a number of the problems that one gets in this most relevant of applications, (2) derive the fitness gradient occurring in the CE from simple fitness return arguments, (3) show explicitly that setting said fitness gradient equal to zero results in the classical marginal value... (More)
This paper should be read as addendum to Dieckmann et al. (J Theor Biol 241:370-389, 2006) and Parvinen et al. (J Math Biol 67: 509-533, 2013). Our goal is, using little more than high-school calculus, to (1) exhibit the form of the canonical equation of adaptive dynamics for classical life history problems, where the examples in Dieckmann et al. (J Theor Biol 241:370-389, 2006) and Parvinen et al. (J Math Biol 67: 509-533, 2013) are chosen such that they avoid a number of the problems that one gets in this most relevant of applications, (2) derive the fitness gradient occurring in the CE from simple fitness return arguments, (3) show explicitly that setting said fitness gradient equal to zero results in the classical marginal value principle from evolutionary ecology, (4) show that the latter in turn is equivalent to Pontryagin's maximum principle, a well known equivalence that however in the literature is given either ex cathedra or is proven with more advanced tools, (5) connect the classical optimisation arguments of life history theory a little better to real biology (Mendelian populations with separate sexes subject to an environmental feedback loop), (6) make a minor improvement to the form of the CE for the examples in Dieckmann et al. and Parvinen et al. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Function valued traits, Pontryagin’s maximum principle, Age-dependent resource allocation, Mendelian take on life history theory, Evolution in periodic environments
in
Journal of Mathematical Biology
volume
74
issue
4
pages
1125 - 1152
publisher
Springer
external identifiers
  • pmid:26586121
  • scopus:84958124373
  • wos:000370269200014
ISSN
1432-1416
DOI
10.1007/s00285-015-0938-4
language
English
LU publication?
yes
id
349ff2f8-79a7-4d83-9eee-6c9a32cd7b27 (old id 8235082)
date added to LUP
2015-12-08 13:31:41
date last changed
2017-07-09 03:51:14
@article{349ff2f8-79a7-4d83-9eee-6c9a32cd7b27,
  abstract     = {This paper should be read as addendum to Dieckmann et al. (J Theor Biol 241:370-389, 2006) and Parvinen et al. (J Math Biol 67: 509-533, 2013). Our goal is, using little more than high-school calculus, to (1) exhibit the form of the canonical equation of adaptive dynamics for classical life history problems, where the examples in Dieckmann et al. (J Theor Biol 241:370-389, 2006) and Parvinen et al. (J Math Biol 67: 509-533, 2013) are chosen such that they avoid a number of the problems that one gets in this most relevant of applications, (2) derive the fitness gradient occurring in the CE from simple fitness return arguments, (3) show explicitly that setting said fitness gradient equal to zero results in the classical marginal value principle from evolutionary ecology, (4) show that the latter in turn is equivalent to Pontryagin's maximum principle, a well known equivalence that however in the literature is given either ex cathedra or is proven with more advanced tools, (5) connect the classical optimisation arguments of life history theory a little better to real biology (Mendelian populations with separate sexes subject to an environmental feedback loop), (6) make a minor improvement to the form of the CE for the examples in Dieckmann et al. and Parvinen et al.},
  author       = {Metz, Johan A Jacob and Staňková, Kateřina and Johansson, Jacob},
  issn         = {1432-1416},
  keyword      = {Function valued traits,Pontryagin’s maximum principle,Age-dependent resource allocation,Mendelian take on life history theory,Evolution in periodic environments},
  language     = {eng},
  month        = {11},
  number       = {4},
  pages        = {1125--1152},
  publisher    = {Springer},
  series       = {Journal of Mathematical Biology},
  title        = {The canonical equation of adaptive dynamics for life histories: from fitness-returns to selection gradients and Pontryagin's maximum principle.},
  url          = {http://dx.doi.org/10.1007/s00285-015-0938-4},
  volume       = {74},
  year         = {2015},
}